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We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…

Combinatorics · Mathematics 2015-03-03 B. S. El-Desouky , Abdelfattah Mustafa

The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.

Number Theory · Mathematics 2009-12-31 Taekyun Kim

The aim of this paper is twofold. The first one is to find several relations between the type 2 higher-order degenerate Euler polynomials and the type 2 higher-order Changhee polynomials in connection with the degenerate stirling numbers of…

Number Theory · Mathematics 2020-04-28 Taekyun Kim , Dae San Kim

In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.

Number Theory · Mathematics 2013-01-23 Taekyun Kim , Dae San Kim

In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.

Number Theory · Mathematics 2024-02-28 Chellal Redha

In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.

Number Theory · Mathematics 2014-03-19 Dae San Kim , Taekyun Kim , Jong Jin Seo

In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.

Number Theory · Mathematics 2010-11-25 Taekyun Kim

In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…

Number Theory · Mathematics 2014-01-28 Hassan Jolany , Mohsen Aliabadi , Roberto B. Corcino , M. R. Darafsheh

Using the methods of classical invariant theory a general approach to finding of identities for Bernulli, Euler and Hermite polynomials is proposed.

Combinatorics · Mathematics 2012-10-02 Leonid Bedratyuk

In this paper, we study some properties of Changhee's q-Bernou lli polynomials which are derived from p-adic invariant integral on Zp. By using these properties, we give some interesting identities related to higher- order q-Bernoulli…

Number Theory · Mathematics 2013-07-02 Jong Jin Seo , Taekyun Kim

In this paper, we investigate some identities of Laguerre polynomials involving Bernoulli and Euler polynomials which are derived from umbral calculus.

Number Theory · Mathematics 2015-06-12 Taekyun Kim

I recent years, many mathematicians studied various degenerate version of some spcial polynomials of which quite a few interesting results were discovered. In this paper, we introduce the type 2 degenerate Bernoulli polynomials of the…

Number Theory · Mathematics 2019-08-20 Taekyun Kim , Lee-Chae jang , Dae San Kim , Han-Young Kim

In this paper, we consider the degenerate Changhee numbers and polynomials of the second kind which are different from the previously introduced degenerate Changhee numbers and polynomials by Kwon-Kim-Seo (see [11]). We investigate some…

Number Theory · Mathematics 2017-08-01 Taekyun Kim , Dae San Kim

In this paper, by using some families of special numbers and polynomials with their generating functions, we give various properties of these numbers and polynomials. These numbers are related to the well-known numbers and polynomials,…

Combinatorics · Mathematics 2023-02-24 Yilmaz Simsek

In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.

Number Theory · Mathematics 2013-02-01 Taekyun Kim , Dae San Kim

In this paper, we give some new and interesting identities which are derived from the basis of Frobenius-Euler. Recently, Simsek et als(see [13]) have given some identities of q-analogue of Frobenius-Euler polynomials related to q-Bernstein…

Number Theory · Mathematics 2012-11-29 Dae San Kim , Taekyun Kim

In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.

Number Theory · Mathematics 2010-07-21 Min-soo Kim , Daeyeoul Kim , Taekyun Kim

The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.

Mathematical Physics · Physics 2007-05-23 Carl M. Bender , Dorje C. Brody , Bernhard K. Meister

In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein polynomials.

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Armen Bagdasaryan , Erdogan Sen

The Peters polynomials are a generalization of Boole polynomials. In this paper, we consider Peters and poly-Cauchy mixed type polynomials and investigate the properties of those polynomials which are derived from umbral calculus. Finally,…

Number Theory · Mathematics 2013-10-09 Dae San Kim , Taekyun Kim